Question

Cho x, y, z > 0 thỏa mãn \(2\sqrt{xy}+\sqrt{xz}=1.\)

Tính Min \(P=\frac{3yz}{x}+\frac{4xz}{y}+\frac{5xy}{z}\)

Answer 1

lon ok

Answer 2

Yes.

Answer 3

Dăm ba mấy dạng kiểu này

Cô si vài cái có gì khó khăn !

\(P=\frac{3yz}{x}+\frac{4xz}{y}+\frac{5xy}{z}\)

\(=\left(\frac{yz}{x}+\frac{zx}{y}\right)+2\left(\frac{yz}{x}+\frac{xy}{z}\right)+3\left(\frac{zx}{y}+\frac{xy}{z}\right)\)

\(\ge2z+3y+6x\)

\(=2\left(x+z\right)+4\left(x+y\right)\)

\(\ge4\sqrt{xz}+8\sqrt{xy}\)

\(=4\left(\sqrt{xz}+2\sqrt{xy}\right)\)

\(=4\)

Dấu "=" xảy ra tại \(x=y=z=\frac{1}{3}\)

Answer 4

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